Fur taken from pit after hesitation (6)
I believe the answer is:
ermine
'fur' is the definition.
(I know that ermine is a type of fur)
'pit after hesitation' is the wordplay.
'pit' becomes 'mine' (mining pit).
'after' says to put letters next to each other.
'hesitation' becomes 'er' (sound made while hesitating - um, er).
'mine' put after 'er' is 'ERMINE'.
'taken from' is the link.
(Other definitions for ermine that I've seen before include "Animal with brown fur that turns white in winter" , "White fur from kind of 25 Across - judges may wear it" , "White fur associated with judges" , "White fur worn by some judges" , "White-coated stoat" .)